Question

How many cubes with edge length of ⅓ inch are needed to fill a rectangular prism that is 3 inches by 1 inch by 1 ⅓ inches?

Answer 1

Answer:

We need 108 cubes to fill the rectangular prism

Step-by-step explanation:

We are given the dimensions of a cube with an edge length of 1/3 inch.

A rectangular prism is to be filled out with those cubes. The dimensions of the prism are 3 inches x 1 inch x 1 1/3 inches.

The fraction 1 1/3 is expressed as:

$1\frac{1}{3}=1+\frac{1}{3}=\frac{4}{3}$

We need to know how many cubes fit in each dimension. It can be found by dividing them by their edge length:

$\displaystyle \frac{3}{\frac{1}{3}}=3*3 =9$

$\displaystyle \frac{1}{\frac{1}{3}}=1*3 =3$

$\displaystyle \frac{\frac{4}{3}}{\frac{1}{3}}=\frac{4}{3}*3=4$

Now we multiply the number of cube per dimension:

9*3*4=108

We need 108 cubes to fill the rectangular prism